Table Of ContentON THE SCALING LAWS FOR JET NOISE IN SUBSONIC AND SUPERSONIC FLOW
M. Kandula*
Dynacs Inc., Kennedy Space Center, FL 32899
B. Vut
NASA Kennedy Space Center, FL 32899
ABSTRACT St = Strouhal number= fdj I uj
T = temperature
The scaling laws for the simulation of noise from
u = velocity
subsonic and ideally expanded supersonic jets are exam-
x = axial distance from the nozzle exit plane
ined with regard to their applicability to deduce full scale
y = radial distance from the jet axis
conditions from small-scale model testing. Important
parameters of scale model testing for the simulation of jet vi = turbulent velocity fluctuation
noise are identified, and the methods of estimating full- W,,, = mechanical power
scale noise levels from simulated scale model data are
addressed. The limitations of cold-jet data in estimating
GREEK SYMBOLS
high-temperature supersonicj et noise levels are discussed.
It is shown that the jet Mach number (jet exit veloc-
Sg= Kronecker delta
itytsound speed at jet exit) is a more general and conven-
ient parameter for noise scaling purposes than the ratio of p = dynamic viscosity
jet exit velocity to ambient speed of sound. A similarity p = density
spectrum is also proposed, which accounts for jet Mach A = wavelength
number, angle to the jet axis, and jet density ratio. The y = isentropic exponent
proposed spectrum reduces nearly to the well-known simi-
f3 = angle from the jet axis
larity spectra proposed by Tam' for the large-scale and the
17 = acoustic intensity
fine-scale turbulence noise in the appropriate limit.
w = solid angle
NOMENCLATURE wf = characteristic frequency of the eddies
A =jet cross sectional area
SUBSCRIPTS
c = sound velocity
dj =jet exit diameter, characteristic length av = average
f =frequency c =chamber condition
f =full scale
F, = thrust
- j =jet
Z = sound intensity = p 2 t pc m = model
Z' = normalized acoustic far field intensity ref = reference condition
L= characteristic length scale of eddies = ambient fluid
00
m = mass flow rate
M = Mach number INTRODUCTION
p = pressure
The generation of noise from turbulent jets is of great
P = sound power= 4m 2Z
practical interest in the design ofjet engines (subsonic and
P'= sound power per unit volume
supersonic civil transport) and the study of launch vehicle
r = distance from the sound source
acoustics. Acoustic loads in a launch vehicle environment
R = gas constant
induce structural vibration of vehicle components, ground
Re = Reynolds number= pjujdj t pj
support structures and equipment in the immediate vicin-
ity of the launch pad. In the design of launch vehicles, it
*Principal Investigator, Associate Fellow AIAA
Thad, Launch Systems Testbed, Member AIAA
1
American Institute of Aeronautics and Astronautics
is highly desirable that data on acoustic loads (near-field DYNAMIC SIMILARITY
and far-field noise levels) be generated both analytically
and from testing of small-scale and full-scale models. A schematic of the jet configuration is shown in Fig.
Since full-scale acoustic and vibration testing is often 1. In general the sound pressure is a function of several
cost-prohibitive, the option of small-scale testing com- variables
bined with analysis methods remains as a practical
alternative.
Noise from subsonic jets is mainly due to turbulent
mixing, comprising the contributions of large-scale and
From dynamic similarity considerations, the sound power
fine-scale structure^.^'^ The turbulent mixing noise is
can be expressed in a dimensionless form as
mainly broadband. In perfectly expanded supersonic jets
(nozzle exit plane pressure equals the ambient pressure),
the large-scale mixing noise manifests itself primarily as
Mach wave radiation caused by the supersonic convection
of turbulent eddies with respect to the ambient fluid. In
imperfectly expanded supersonicj ets, additional noise is
generated on account of broadband shock noise and
screech tones. In the above, the jet Mach number Mi,t he Strouhal
number St ,a nd the Reynolds number Re are defined by
Scale models are often used in early design stage as a
means of predicting the acoustic environment associated
fdj
with flight vehicles. A detailed knowledge of the mecha- M i = -u j , St=-, Re=- Pjujdj (3)
nisms of noise generation and noise radiation by jets is
essential in designing a scale model of the noise ~ource.~
In order to ensure complete similarity between model and
where sound speeds cj and c, in the jet and the ambient
full scale, we need to ensure similarity of flow, noise gen-
are defined by
eration, and noise propagation.
In practice, it is generally difficult to duplicate (simu-
late) all the characteristic parameters in the scale model.
Model testing with even smaller rocket engines requires
MECHANISMS OF NOISE GENERATION AND
extensive safety precautions. Heated jet facilities also
THEORETICAL CONSIDERATIONS
involve considerable complexity and cost. The use of less
expensive facilities or lower gas temperatures, for exam-
Isothermal Jets
ple, would considerably simplify model te~ting.~T he
ability to conduct a scale model test with a substitute gas
Lighthill’s Theory for Subsonic Jets
(air, nitrogen, helium, etc.) results in considerable savings
(reduced costs of test facilities, test time) and advantages.
Lighthill 2*3 has shown by an acoustic analogy that
For example, helium-air mixture jets for simulating high-
aerodynamic sound is a consequenceo f turbulence, which
temperature effects have been studied by Kinzie and
provides a quadrupole source distribution in an ideal gas
Mchughlin.’ These substitute gas tests require some
at rest. The dominant effect of steady low-speed solenoi-
compromise of the actual physics of the hot jet.
dal convection has been accordingly developed in terms
of an inhomogeneous wave equation (derived on the basis
In the absence of an exact match between the dimen-
of continuity and momentum equations) of the form6
sionless parameters of the scale model and the full scale, a
detailed knowledge of the functional relationship respect-
a 2 ~ ,
ing the various parameters is essential to aid in the inter- -a-2 p
c,v p=- axi ax (5a)
pretation of scale model data to predict the full-scale envi- at2
ronment. The purpose of this report is to review the scal-
ing laws for simulating noise from both subsonic jets and
where the LHS represents the acoustic wave propagation,
ideally expanded supersonicj ets on the basis of both theo-
and the RHS contains the sources that generate the noise
retical considerations and experimental data.
field. The quantity Tu is the Lighthillian acoustic tensor
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where C(M,,B)=[(l-M,cosO)2 +a2M:]” (IO)
Here 0 is the angle from the jet axis, M, the convection
where vi is the velocity, p the local pressure, and zg the Mach number, and a accounts for finite decay time of the
viscous compressive stress tensor. Here the first term eddies. The convection Mach number M, is defined as
represents the contribution of momentum flux, which is the effective Mach number of the convecting turbulent
important in cold flow (no marked temperature differ-
eddies in the mixing regions, and may be approximately
ences exist), so that only the first term is retained:
related to the jet Mach number in a stationary ambient as
Lighthill’ obtained a formal solution of the Eq. (5a) The quantity a is defined as
with the aid of Green’s functions. By the application of
dimensional analysis to the formal solution, the acoustic
power from isothermal subsonic jets is theoretically a 2 =u2fL2 t(nc 2, )= const (1 Ib)
shown to be
where uf and L represent the characteristic frequency
and length scale of the eddies, respectively. An integra-
tion of the sound power over all solid angles yields that
where K is a proportionality constant, called the acoustic
power ~oefficient.~T his relation is the celebrated
Lighthill’s u; law for subsonic jets. Subsonic cold-jet
data confirm the uj dependence, as seen in Fig. 2, which
so that
is adapted from Ffowcs Williams? as reproduced from
Chobotov and Powell.* The acoustic efficiency for sub-
sonic cold jets is thus expressed as
P acoustic power
q=-= a u; (7)
W,,, jet mechanical power
represents the mean amplification factor.”
where the jet mechanical power W, can be expressed in
terms of the thrust Ft as The nonsingular factor C-’ in Eq. (9) replaces the
idealized factor (1 - M, COS^)-^ introduced by
W, =O.SF,uj, Lighthill? amounting to very large decay time of eddies,
)av
thereby leading to (CY5 = (I + Mz)/G - M: . The
exponent was corrected by Ffowcs Williams” from -6 to
-5 . It is shown that the simple expression of Lighthill
with the expression for the thrust applicable for perfectly exaggerates the directivity by up to 10 dB at turbojet flow
expanded jets. speeds.”
Effect of Source Convection Fig. 3 shows the variation of the mean convective
amplification factor with M, for a typical value of
The above theory holds only for stationary sources. a = 0.4. This amplification factor is seen to slowly in-
Since quadrupoles are convecting downstream, the effect
crease with M, in the subsonic range, providing a u8j
of moving sources on the direction of noise radiation is
accounted for by a convection dependence in the low speed region.” It ultimately ap-
proaches Mc-5 dependence at high Mach numbers.
P(0)= Kp,uj 7.5 c, -5 d, C -5 (9)
A polar plot of the variation of directivity ofjet noise
(relative to 8 = 90 deg) at various Mach numbers is ex-
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hibited in Fig. 4a. Fig. 4b presents a linear plot of the efficiency must ultimately diminish like uy3’2o r the
directivity of the jet noise considered in Fig. 4a. The di-
rectivity at increased Mach numbers is clearly evident. sound power as u?’” There is very limited data at very
Experimental data suggest the existence of a refractive dip
high Mach numbers to provide a validation of this theory.
close to the jet axis as a result of refraction by the mean
Also at very high Mach numbers (characteristic of hyper-
flow. A discussion of the effects of refraction in the scal-
sonic regime), real gas effects and property variations can
ing law is beyond the scope of the present paper.
become significant such that the accuracy of the theory
Directivity and spectral effects of shear-noise (due to joint
becomes questionable.
contribution of turbulence and mean flow) is also not con-
sidered here, and only self-noise due to turbulence is ac-
Based on the foregoing discussion, we may roughly
counted for.
summarize the sound power level dependence in super-
sonic speeds as follows:
Supersonic Jets
1.0 < M < 1.5
An examination of Fig. 2 suggests that the ujdj law
1.5<M<2.5 (15)
of Lighthill for subsonic flow breaks down at high exhaust
velocities, where the convection velocities of the eddies in
2.5 < M < 5
the turbulent mixing region approaches supersonic values.
At the high exhaust velocities of present today rocket en-
gines, this law predicts a physically unrealistic result that Spectral Distribution
over 100% of the jet propulsive power is converted to
first derived a similarity law for sound
noise.” Experimental data suggest a u6 dependence of
power spectrum of the form
the sound power level for supersonic jets of low Mach
4
numbers ( Mj = 1 to 1S ). At higher Mach numbers, a uj
dependence is noted by the measurements at Mach 2.5
(Ref. 13), as reviewed by S~therland.’T~h ese trends are
consistent with the measurements by Cole et al.,” as re-
viewed by McInerny.16 At still larger Mach number (in
excess of about 2.5), a uj dependence of sound power
level is observed. The uj dependence of sound power where fp represents the peak frequency value, Ti the
implies a constant acoustic efficiency independent of jet local time-averaged density and C is defined by Eq. (lo).
velocity. Ribner” proposed for the self noise a semiempirical spec-
trum of the form
As noted by Ffowcs william^,^ possible mechanism
of sound generation by supersonic shear layers is quite
different from that indicated by Lighthill’ for low-speed
subsonic jets. Ffowcs Williams extended Lighthill’s the-
ory for high-speed solenoidal convection and predicted a
u3d ependence of jet noise at high supersonic Mach num- 2
-V
where H(v)= v = fCl f p (17b)
bers.’ A uj dependence is also indicated by Tam.17 (1+“’Y ’
These predictions are in qualitative agreement with the
data at high supersonic flow. The departure from the u! which provides the asymptotic behavior according to Eq.
(16).
dependence at supersonic speeds may be partly attributed
to compressibility effects, causing a reduction in source
On the basis of a detailed study of jet noise data for
strength.” At increased Mach numbers, there is a reduc-
sound power spectrum for supersonic and subsonic jets
tion of transverse velocity fluctuations in the mixing layer,
(both hot and cold jets), Tam et al.’ postulated (discov-
as indicated by the data of Goebel and Dutton” and pre-
ered) the existence of two universal similarity spectrum
dicted in Kandula and Wilcox.
functions F and G , such that the overall jet noise spec-
trum is expressed as
Phillips” proposed an asymptotic theory for very
high values of uj lc, , according to which the acoustic
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(O< Mj<0.9) at a fixed jet velocity, an increase in jet
where F(f / f ~is) a s pectrum for the large-scale turbu-
temperature diminishes the sound power level (Fig. 6).
lencelinstability waves ( characteristic of Mach wave ra- On the other hand, at a given jet Mach number Mj , an
)
diation), and C(f / ff is the spectrum for the fine-scale
increase in jet temperature enhances the sound power
turbulence.u The frequencies f and f f correspond level as shown by Morgan et al. (see Fig. 7). Kinzie and
McLaughlin’ note that significant differences exist be-
respectively to the peaks of the large-scale turbulence and
tween noise from moderately heated supersonic jets and
fine-scale turbulence. These spectrum functions are nor-
. unheated supersonic jets. Heated air data of Seiner et al.”
malized such that F(1) = G(l) = 1 Empirical correlations
at Mj= 2 suggest that the peak OASPL is higher at higher
are proposed for the amplitudes A and B , and the peak
frequencies of the two independent spectra as a function temperatures (6 dB increase as Tj increases from 313 to
of the jet operating parameters uj lc,,T, IT, and the 1534 K), as demonstrated in Fig. 8.
inlet angle 8 . It is shown that the noise due to large-scale
structure is dominant at small angles to the jet axis and Experiments by Tanna28 for cold and hot subsonic
that the fine-scale structure is dominant in the forward and supersonicj ets show that the spectral content of noise
quadrant. from hot jets is fundamentally different from that of cold
jets. There is an order-of-magnitude variation in peak
Fig. 5 displays the two universal similarity spectra of frequency and amplitude, as displayed in Fig. 9, adapted
Tam for large-scale turbulence noise and fine-scale turbu- from Fortune and Gervais 24.
lence noise.’ For comparison purposes, the empirical
spectrum due to Ribner” is also presented. It is interest- Analvses and Correlations
ing to note that the Ribner spectrum matches well with the
large-scale turbulence noise spectrum for frequencies be- In the presence of density differences between the jet
low the peak frequency, whereas it compares better with fluid and the ambient fluid (such as helium jets in air), the
3
Tam’s fine-scale turbulence noise spectrum beyond the corresponding acoustic power is proposed by Lighthill as
peak frequency except at very large frequencies.
P = Kpj2p --1 U8~ C-5 -d 2j
Heated Jets
Experimental Considerations since the Lighthill’s stress tensor contains a factor pi.
With regard to the role of jet temperature, Lighthill points
Whereas cold jets have been the subject of many in- out that inhomogeneities in temperature amplify the sound
vestigations, relatively little research has been devoted to due to turbulence, just as shear affects high-frequency
the topic of heated jets.24 While in commercial transport components of the jet noise. According to Lighthill, the
applications (turbojets), the jet temperature is of the order effects of velocity and temperature cannot be separated.
of 1000 OF ( Mj= 0.6 to 0.9),t he temperatures in rocket
exhausts are considerably higher and are of the order of Mani29930h as shown, with the aid of a slug flow ap-
proximation, that mean density gradients act to generate
2000 (Mi= 2.5 to 3.5). Although cold air jets can be
O F
dipole and monopole source terms, which produce
used to determine differences in a noise field due to geo-
M and M dependence at high jet temperatures for con-
metric changes, the use of cold air jets to establish abso-
stant value of (jet temperature - ambient temperature),
lute values of a full-scale noise field is considered not
where M denotes the ratio of jet velocity to ambient
fea~ibleC.~o ld-air tests are thus good to indicate qualita-
sound speed.
tive differences in the acoustic field but are only indica-
tive of the order of magnitude of the actual phenomena of
noise reduction. Morfey et al. l8 developed scaling laws for both quad-
rupole and dipole components of turbulent mixing. They
proposed an additional mixing noise due to dipole source
Data on scale models generally suggest a 5-10 dB
at high jet temperatures and suggested the following rela-
difference between cold- and hot-jet tests. According to a
review by Fisher et ai.?’ for a constant mean velocity of tion for the normalized acoustic far-field intensity I’ :
the jet, the acoustic levels increase with an increase in
mean temperature of the jet for Mj < 0.7 and decrease
with an increasing temperature if Mi > 0.7 . According
to the data of Narayanan et a1.,26 for subsonic jets
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where n = 6.4 + 1.2/(TC .
It is seen from the above relations that the jet tem-
perature has strong effect on the velocity component. In
the case of large-scale turbulence, the velocity exponent
n for cold jets (T, /T, = 1) is approximately equal to
1
9.5, which is somewhat larger than 8, as predicted by the
[
Lighthill's acoustic analogy. In the case of fine-scale tur-
where Z ' =- pL - , AT=Tj-T, (21) bulence, the velocity exponent n reduces to 7.6 for cold
PX
dj
jets (T, /T, = l),i n very close agreement with the well-
known subsonic jet value of 8, as predicted by Lighthill's
The dipole term is based on theoretical considerations of
theory. At a jet temperature ratio of 2, the value of the
sound generation by convected density inhomogeneities.
exponent reduces to 6.85.
It is suggested that, in order to generalize the prediction
scheme, the temperature ratio Tj IT, be replaced by
Recently, Massey et al. 32 suggested a correction fac-
tor for the temperature effects, as based on their data over
(pj / pm)- I, the density ratio being the dynamically sig-
a range of M = 0.6 to 1.2 for rectangular jets issuing from
nificant quantity. converging nozzles:
31
On similar grounds, Liley proposed the existence of
an additional dipole source term arising from density fluc-
tuations (due to temperature fluctuations) and suggested
[
that the sound power per unit volume of turbulence can be
expressed as = f1 log[ u-j:mum)]
where Ai represents the jet cross sectional area, and STP
referes to the standard conditions.
According to Liley, the dipole term dominates the quad-
Calculations by the present authors, using OVER-
rupole term at high speeds.
FLOW Navier-Stokes CFD code?3 have shown that the
length of the supersonic core decreases with an increase in
From a detailed study of axisymmetric, supersonic,
jet temperature, at a constant jet Mach number of 2 and
high-temperature jet noise data of NASA Langley Re-
constant ambient temperature (Fig. 10). This suggests
search Center, including that of Seiner et al.: ' Tam et al.
that an increase in jet temperature not only introduces
'proposed correlations for the peak sound pressure level
dipole sources but also alters the quadrupole source dis-
(at 90 deg to the jet axis) for the large-scale turbulence
tribution by shortening the core length.
and fine-scale turbulence. For the large-scale turbulence,
the correlation for the amplitude A (in dB/Hz) is pro-
PROPOSED SCALING LAWS
posed as
Sound Power
lOlog(A/p$) = 75 + 46/(T, /T,)0'3
(23) Based on a detailed study of the above considerations
+
lolog(uj /cmp
concerning experimental data and theoretical analyses,
refinements to the scaling laws for jet noise are proposed
where n = 10.06 - O.495/(Tc/ Tm) as follows. In accordance with Lighthill-Ffowcs
Williams-Ribner formulations, the following expression
The amplitude for the fine-scale turbulence, B (in for the sound power level is proposed for both subsonic
and supersonic flow:
dB/Hz) is recommended as
lOlog(B/p&) = 83.2 + 19.3/(TC
(24)
+
lolog(uj /cmp
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G2 are ignored. Eqs. (31a) and (31b) illuminate the fun-
damental difference in temperature scaling of sound
power. Eq. (31a) suggests an amplification of sound
power with increased jet temperature for a fixed value of
Mj , while Eq. (31b) suggests a decreased value of
sound power with an increase in jet temperature for a con-
.
stant value of uj
where K1i s a proportionality constant, GI is the directiv-
ity factor (owing to source convection), and G2 accounts Similarity Spectrum
for the distribution of the sound power. The directivity
factor is essentially the same as given by Eq. (10) in ac- A single similarity spectrum is also proposed here to
cordance with Lighthill-Ffowcs Williams-Ribner formula- apply to both subsonic and supersonic flow and to account
tion: for both the fine-scale turbulence and turbulence structure
associated with Mach wave radiation. A’semiempirical
spectrum is propose here as
where a value of Q = 0.4 is considered. The convective
Mach number M, is related to the jet Mach number as
1
M, = 0.55Mj = 0.55(uj lcj (28) where a = b.2 + exp(- 4M, cosB(Pi / p,))10.35 (32b)
Eq. (26) can also be recast in an alternative form as
The density ratio parameter pi / pm indirectly takes into
account the effects of jet temperature on the quadrupole
character of the sound source.
The proposed expression is based on Von Karman-
type interpolation formula for isotropic turbulence34a s
suggested by Saffman.35 V~n-Karmanor~ig~i nally pro-
posed a spectrum of the form
For a thermally perfect gas, the density ratio is related
to the temperature ratio by
which covers the range between the permanent largest
eddies of f -law (as f + 0 ) and the Kolmogorov iner-
Thus for an ideal gas, the temperature dependence of
tial ~ubrange~~characterizbeyd the f -5/3 law at very
sound power at a constant value of jet Mach number can
.
large values of f Following Saffman, considering a
be characterized as
+
f -2 law at k 0, Hinze3’ suggests a spectrum of the
form
On the other hand, for a constant jet velocity, the ratio of
sound power becomes
1
(pf /pz)=( pjl/ p2)=( Tj2/ Til uj = const. (31b)
valid for the turbulent transport of both a vector (velocity
and momentum) and a scalar quantity.
where any differences in Mj influencing the directivity
and spectral distribution through the factors GI and The proposed expression, given by Eq. (32), is of
more general form, capable of describing the spectrum at
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American Institute of Aeronautics and Astronautics
low and high Mach numbers and accounting for the direc- noted as the jet Mach number increases from 0.2 to 1.0
tivity effects and departures from isothermality. The im- (see data of Fig. 2 at uj =200 ft/s and uj =IO00 fds).
port of the proposed spectrum is that at high jet Mach
numbers the broadband turbulence spectrum degenerates
Fig. 11 also suggests that, at a given Mi,O ASPL
to the narrowband spectrum typical of large-scale turbu-
lence governing Mach wave radiation. It is seen that for depends only on the temperature ratio, as indicated by Eq.
the isothermal case, the present spectrum reduces to the (31a). Comparison of this theory with the data of Mor-
following form: gan4s uggests that, at Mj = 1 and a temperature ratio of 3
(jet temperature increased from 60 to 1120 the ob-
OF),
served increase in OASPL is about 13 dB, while the pre-
sent scaling law provides a value of 14.3. Referring to the
subsonic data of Narayanan,26a s seen in Fig. 6, at a con-
stant value of uj / c, = 0.89 1 ,a drop of OASPL of about
5 dB is noted as the jet temperature is increased form 83
to 1000 This compares favorably with a predicted
OF.
value of about 4.3 dB according to the present scaling law
(34)
[Eq. ( 3 ~ 1 .
Recent Direct Numerical Simulation (DNS) data by
Similarity Spectrum
Bodony and Lele3’ suggest that, at Mi = 1.2 , the spec-
trum is of the form f-3.33 at large values of wave num- The variation of similarity spectrum with Mach num-
ber at a constant value of 6’ = 20 deg is provided in Fig.
ber, which is close to the present result of f-3.074.
12a. Also shown in this plot are the similarity spectra of
Tam’ for large-scale turbulence noise and fine-scale tur-
With regard to noise spectrum due to fine scale turbu- bulence noise derived on the basis of experimental data of
lence, Morris and Fara~sarte~ce~n tly presented a detailed NASA Langley Research Center. The results indicate that
comparison of of predictions from acoustic analogy theo- at large values of Mach number, the spectrum becomes
ries and by the method of Tam and A~riaulitn~vo~l ving closer to the similarity spectrum of Tam for large-scale
adjoint Green’s function for the linarized Euler equation. turbulence. As the jet Mach number is reduced, the pro-
posed spectrum becomes progressively broader and ap-
RESULTS AND DISCUSSION proaches the similarity spectrum of Tam for fine-scale
turbulence. The intersection of the fine-scale spectrum
Overall Sound Power with the large-scale spectrum at high frequencies, as ob-
served in the similarity spectra of Tam, is absent in the
The variation of OASPL with the jet Mach number is present predictions. Spectral data of Massey et al. 32 at
portrayed in Fig. 11 with the jet temperature ratio as a 6’ = 40 deg for a Mach number range of 0.6 to 1.2 qualita-
parameter. The isothermal result is obtained from Eq. tively support this trend.
(13). and the temperature effects are evaluated from Eq.
(3 la). The calculations correspond to the perfectly ex- Referring to Fig. 12b, a comparison of similarity
panded jet. For convenience, the data are plotted with
spectra at Mj = 2 for various angles to the jet axis, we
reference to the OASPL value at Mj = 1. As is to be
see that as the angle is increased from 20 to 90 deg, the
expected, the OASPL transitions from a uj dependence proposed spectra shifts from a narrow band to a broad
band and isgenerally bounded by the similarity spectra of
in subsonic flow to uj at large supersonic Mach numbers. Tam. The comparisons suggest that the narrowband spec-
The transition region corresponds to a range of Mi =1.5 trum characterizing the large-scale turbulence noise of
Mach wave radiation is likely a perturbation from the
to 3.0, which in turn translates to a convective Mach num-
fine-scale spectrum. Some evidence to this effect is found
ber range of 0.825 to 1.65. Although the calculations are
from the recent experimental data of Hileman and
shown for jet Mach numbers of 10, they should be used
Samimy4, which suggest a rather continuous transition
with caution for jet Mach numbers in excess of about 5
from the narrowband spectrum to a broadband spectrum
(hypersonic flow) where real gas effects (including disso-
as the angle of a Mach 1.3 jet is increased from 20 to 90
ciation) can become significant. The results for the iso-
deg.
thermal jets ( Tj /T, = 1) appear to be in good agreement
with the available data (see Fig. 2). For example, for the Finally, the effect of jet temperature on the sound
isothermal jet, an increase of OASPL of about 60 dB is power spectra is highlighted in Fig. 12c for M = 2 and
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8 = 20 deg. Consistent with the measured data, as the jet
temperature is increased, the spectrum progressively shifts Lighthill, M.J., “On sound generated aerodynamically,
from a narrowband spectrum to a broadband spectrum. 11. Turbulence as a source of sound,” Proc. Roy. SOC. A.,
222,1954, pp. 1-32.
CONCLUSION
4Morgan, W.V.,Sutherland,L.C., andYoung,K.J., “The
A review of the scaling and similarity laws applied to use of acoustic scale models for investigating near field
jet noise suggests that proper care needs to be exercised in noise of jet and rocket engines,” WADD Technical Report
extending small-scale test data to full-scale application. 61-178, Wright-Patterson Air Force Base, Ohio, 1961.
While the phenomenon of noise generation and propaga-
tion in subsonic flow has been satisfactorily understood, Kinzie, K.W. and McLaughlin, D.K., “Measurements of
theory of noise generation in highly supersonic flow is Supersonic HeliudAir Mixture Jets,” AIAA J., Vol. 37,
relatively less understood. The effect of jet temperature in NO. 11,1999, pp. 1363-1369.
supersonic jets leads to additional complication in the
understanding of jet noise. The issue of highly supersonic Goldstein, M.E., Aeroacoustics, McGraw-Hill, New
jets at high temperature, typical of launch vehicles, re- York, 1976.
quires further experimental and theoretical study.
’
Ffowcs Williams, J.E., ‘The noise form turbulence con-
With the aid of scaling laws for jet noise proposed vected at high speed,” Proc. Roy. SOC.A ., 255,469,1963.
here, it has been demonstrated that the jet Mach number,
rather than the ratio of jet velocity to ambient sound ve- Chobotov, V. and Powell, A., “On the prediction of
locity, is the proper scaling parameter for correlating high- acoustic environments from rockets,” Rama-Wooldridge
temperature jet noise. The effect of jet temperature is Corp. Rept. E.M.-7-7, 1957.
accounted for by Lighthill’s suggestion through the
changes in the density factor in the quadrupole field. No Ribner, H.S., “New theory of jet-noise generation, direc-
account, however, was considered as to the importance of tionality and spectra,” J. Acoust. SOC. Amer., Vol. 31,
diploes and monopoles on the sound field at high jet tem- 1962, pp. 245-246.
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tion. The present study, however, suggests that significant lo Ribner, H.S., “The generation of sound by turbulent
jet temperature effects exist insofar as the quadrupole jets,” Advances in Applied Mechanics, Academic Press,
source distributions are concerned. Vol. 8, 1964, pp. 103-182.
A continuous similarity spectra is also proposed that I1 Ffowcs Williams, J.E., “Some thoughts on the effects of
is generally bounded by the similarity spectra proposed by aircraft motion and eddy convection on the noise from air
Tam for large-scale and fine-scale turbulence. Effects of jets,” Univ. of Southampton, Dept. of Aer./Astro., USAA
Mach number and angle from the jet axis are taken into Rept. 155, 1960.
account in the directivity factor, while the effects of Mach
number, angle from the jet axis and temperature are ac- l2 Potter, R.C., and Crocker, M.J., “Acoustic prediction
counted for in the similarity spectra. The resulting predic- methods for rocket engines, including the effects of clus-
tions are in general agreement with the available data. tered engines and deflected exhaust flow,” NASA-CR-
566,1960.
ACKNOWLEGEMENT
l3 Hoch, R.G. et ai., “Studies of the influence of density
This work is supported by funding from Air Force on jet noise,” First International Symposium on Air
Research Laboratory, Wright-Patterson Air Force Base, Breathing Engines, June 1972.
Ohio, with Gregory Moster as the technical monitor.
l4 Sutherland, L.C., “Progress and problems in rocket
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